Gangming Luo

Computational methods for ultrasonic bone assessment

Ultrasound has been proposed as a means to noninvasively assess bone and, particularly, bone strength and fracture risk. Although there has been some success in this application, there is still much that is unknown regarding the propagation of ultrasound through bone. Because strength and fracture risk are a function of both bone mineral density and architectural structure, this study was carried out to examine how architecture and density interact in ultrasound propagation. Due to the difficulties inherent in obtaining fresh bone specimens and associated architectural and density features, simulation methods were used to explore the interactions of ultrasound with bone. A sample of calcaneal trabecular bone was scanned with micro-CT and subjected to morphological image processing (erosions and dilations) operations to obtain a total of 15 three-dimensional (3-D) data sets. Fifteen two-dimensional (2-D) slices obtained from the 3-D data sets were then analyzed to evaluate their respective architectures and densities. The architecture was characterized through the fabric feature, and the density was represented in terms of the bone volume fraction. Computer simulations of ultrasonic propagation through each of the 15 2-D bone slices were carried out, and the ultrasonic velocity and mean frequency of the received waveforms were evaluated. Results demonstrate that ultrasound propagation is affected by both density and architecture, although there was not a simple linear correlation between the relative degree of structural anisotropy with the ultrasound measurements. This study elucidates further aspects of propagation of ultrasound through bone, and demonstrates as well as the power of computational methods for ultrasound research in general and tissue and bone characterization in particular.

Relationship between plain radiographic patterns and three- dimensional trabecular architecture in the human calcaneus.

Abstract: The purpose of this study was to determine the relationship between three-dimensional (3D) trabecular structure and two-dimensional plain radiographic patterns. An in vitro cylinder of human calcaneal trabecular bone was three-dimensionally imaged by micro-CT using synchrotron radiation, at 33.4 μm resolution. The original 3D image was processed using 14 distinct sequences of morphologic operations, i.e., of dilations and erosions, to obtain a total of 15 3D models or images of calcaneal trabecular bone. These 15 models had distinct densities (volume fractions) and architectures. The 3D structure of each calcaneal model was assessed using mean intercept length (fabric), by averaging individual fabric measurements associated with each medial-lateral image slice, and determining the relative anisotropy, R3D, of the structure. A summated pattern or plain radiograph was also computed from the 3D image data for each calcaneal model. Each summated pattern was then locally thresholded, and the resulting two-dimensional (2D) binary image analyzed using the same fabric analysis as used for the 3D data. The anisotropy of the 2D summated pattern was denoted by Rx-ray. The volume fractions of the 15 models ranged from 0.08 to 0.19 with a mean of 0.14. The medial-lateral anisotropies, R3D, ranged from 1.38 to 2.54 with a mean of 1.88. The anisotropy of the 2D summated patterns, Rx-ray, ranged from 1.35 to 2.18 with a mean of 1.71. The linear correlation of the 3D trabecular architecture, R3D, with the radiographic trabecular architecture, Rx-ray, was 0.99 (p<0.0001). This study shows that the plain radiograph contains architectural information directly related to the underlying 3D structure. A well-controlled sequential reproducible plain radiograph may prove useful for monitoring changes in trabecular architecture in vivo and in identifying those individuals at increased risk of osteoporotic fracture.

Finite element analysis of heel pad with insoles

To design optimal insoles for reduction of pedal tissue trauma, experimental measurements and computational analyses were performed. To characterize the mechanical properties of the tissues, indentation tests were performed. Pedal tissue geometry and morphology were obtained from magnetic resonance scan of the subjects foot. Axisymmetrical finite element models of the heel of the foot were created with 1/4 of body weight load applied. The stress, strain and strain energy density (SED) fields produced in the pedal tissues were computed. The effects of various insole designs and materials on the resulting stress, strain, and SED in the soft pedal tissues were analyzed. The results showed: (a) Flat insoles made of soft material provide some reductions in the maximum stress, strain and SED produced in the pedal tissues. These maximum values were computed near the calcaneus. (b) Flat insoles, with conical/cylindrical reliefs, provided more reductions in these maximum values than without reliefs. (c) Custom insoles, contoured to match the pedal geometry provide most reductions in the maximum stress, strain and SED. Also note, the maximum stress, strain and SED computed near the calcaneus were found to be about 10 times the corresponding peak values computed on the skin surface. Based on the FEA analysis, it can be concluded that changing insole design and using different material can significantly redistribute the stress/strain inside the heel pad as well as on the skin surface.

Ultrasound simulation in the distal radius using clinical high-resolution peripheral-CT images.

The overall objective of this research is to develop an ultrasonic method for noninvasive assessment of the distal radius. The specific objective of this study was to examine the propagation of ultrasound through the distal radius and determine the relationships between bone mass and architecture and ultrasound parameters. Twenty-six high-resolution peripheral-CT clinical images were obtained from a set of subjects that were part of a larger study on secondary osteoporosis. A single midsection binary slice from each image was selected and used in the two-dimensional (2D) simulation of an ultrasound wave propagating from the anterior to the posterior surfaces of each radius. Mass and architectural parameters associated with each radius, including total (trabecular and cortical) bone mass, trabecular volume fraction, trabecular number and trabecular thickness were computed. Ultrasound parameters, including net time delay (NTD), broadband ultrasound attenuation (BUA) and ultrasound velocity (UV) were also evaluated. Significant correlations were found between NTD and total bone mass (R2 = 0.92, p < 0.001), BUA and trabecular number (R2 = 0.78, p < 0.01) and UV and trabecular bone volume fraction (R2 = 0.82, p < 0.01). There was only weak, statistically insignificant correlation (R2 < 0.14, p = 0.21) found between trabecular thickness and any of the ultrasound parameters. The study shows that ultrasound measurements are correlated with bone mass and architecture at the distal radius and, thus, ultrasound may prove useful as a method for noninvasive assessment of osteoporosis and fracture risk.

ULTRASONIC ASSESSMENT OF THE RADIUS IN VITRO

The overall objective of this research is to develop an ultrasonic system for noninvasive assessment of the distal radius. The specific objective of this study was to examine the relationship between geometrical features of cortical bone and ultrasound measurements in vitro. Nineteen radii were measured in through transmission in a water bath. A 3.5 MHz rectangular (1 cm x 4.8 cm) single element transducer served as the source and a 3.5 MHz rectangular (1 cm x 4.8 cm) linear array transducer served as the receiver. The linear array consisted of 64 elements with a pitch of 0.75 mm. Ultrasound measurements were carried out at a location that was 1/3rdrd of the length from the distal end of each radius and two net time delay parameters, tau(NetDW) and tau(NetCW), associated with a direct wave (DW) and a circumferential wave (CW), respectively, were evaluated. The cortical thickness (CT), medullar thickness (MT) and cross-sectional area (CSA) of each radius was also evaluated based on a digital image of the cross-section at the 1/3rd location. The linear correlations between CT and tau(NetDW) was r = 0.91 (p < 0.001) and between MT and tau(NetCW) - tau(NetDW) was r = 0.63 (p < 0.05). The linear correlation between CSA and a nonlinear combination of the two net time delays, tau(NetDW) and tau(NetCW), was r = 0.95 (p < 0.001). The study shows that ultrasound measurements can be used to noninvasively assess cortical bone geometrical features in vitro as represented by cortical thickness, medullar thickness and cross-sectional area.

On the relative contributions of absorption and scattering to ultrasound attenuation in trabecular bone: a simulation study

Ultrasound has been proposed as a means to non-invasively assess bone and particularly bone strength and fracture risk. Although there has been some success in this application, there is still much that is unknown regarding the propagation of ultrasound through bone. Because strength and fracture risk are a function of bone mineral density as well as architectural structure and tissue quality, this study was carried out to further elucidate the mechanisms of interaction between ultrasound and bone. Frequency-dependent attenuation of an ultrasound wave in trabecular bone has been shown to be strongly dependent on bone mass and architecture and is currently used in several clinical devices for bone assessment. Since attenuation is due to both absorption by the biological tissues per se and scattering, it is of interest to understand the relative contributions of each. A sample of calcaneal trabecular bone was scanned with micro-CT and subjected to morphological image processing (erosions and dilations) to obtain a total of 11 three-dimensional (3D) date sets. Eleven two-dimensional (2D) slices obtained from the 3D data sets were then analyzed to evaluate their bone volume fractions (VF). Computer simulations of ultrasonic propagation through each of thru 11 2D slices, which varied in VF from 0.088-0.181, were carried out in one of two modes. In the first instance, the component tissue (i.e., marrow and bone) were lossy, while in the second set of simulations the component tissues were lossless. In both cases the slope of the attenuation was computed over the frequency range 300 kHz - 900 kHz for the entire data set. Results obtained showed an average reduction in the attenuation slope of only 4.4% (SD=1.8%) in the lossless case as compared (pairwise) with the lossy case. This data indicates that scattering is the primary mechanism in trabecular bone with respect to overall attenuation measurements, and further suggests that models relating scattering to bone architecture and mass should be developed to further enhance the ability of ultrasound to non-invasively access bone.

A poisson process model for hip fracture risk

The primary method for assessing fracture risk in osteoporosis relies primarily on measurement of bone mass. Estimation of fracture risk is most often evaluated using logistic or proportional hazards models. Notwithstanding the success of these models, there is still much uncertainty as to who will or will not suffer a fracture. This has led to a search for other components besides mass that affect bone strength. The purpose of this paper is to introduce a new mechanistic stochastic model that characterizes the risk of hip fracture in an individual. A Poisson process is used to model the occurrence of falls, which are assumed to occur at a rate, λ. The load induced by a fall is assumed to be a random variable that has a Weibull probability distribution. The combination of falls together with loads leads to a compound Poisson process. By retaining only those occurrences of the compound Poisson process that result in a hip fracture, a thinned Poisson process is defined that itself is a Poisson process. The fall rate is modeled as an affine function of age, and hip strength is modeled as a power law function of bone mineral density (BMD). The risk of hip fracture can then be computed as a function of age and BMD. By extending the analysis to a Bayesian framework, the conditional densities of BMD given a prior fracture and no prior fracture can be computed and shown to be consistent with clinical observations. In addition, the conditional probabilities of fracture given a prior fracture and no prior fracture can also be computed, and also demonstrate results similar to clinical data. The model elucidates the fact that the hip fracture process is inherently random and improvements in hip strength estimation over and above that provided by BMD operate in a highly “noisy” environment and may therefore have little ability to impact clinical practice.

Ultrasound simulation for 3D-axisymmetric models

Development of ultrasound nondestructive evaluation testing (NDT) techniques has involved a combination of both analytic and experimental methods. In contrast, relatively little software exists for ultrasound simulation in NDT, particularly in comparison to that existing for stress-strain and electromagnetic areas. This paper describes new software for simulating the full (longitudinal and shear) solution to the three-dimensional (3D) axisymmetric wave equation. The simulation software is able to model both liquids and solids, and also accounts for losses using a classic viscoelastic model. The program computes the solution using a finite difference time domain algorithm, and evaluates the displacement vector at each (discrete grid) point of the object. Sources and receivers may be placed anywhere in or on the object, which is assumed to be cylindrical. A comparison of the on-axis diffraction pattern results obtained with the simulation software show excellent agreement with analytic results. Results using a cladded rod are also presented. This software should help to broaden the use of computational methods in ultrasonic NDT and in ultrasonics in general.

Computational methods for NDT

Development of ultrasound nondestructive evaluation techniques (NDT) has involved a combination of both analytic and experimental methods. In contrast, relatively little work has been done on the use of computational methods for experimental design and analysis in NDT. This is due to the relative lack of availability of software for such computations. While computational methods and associated software implementations abound in the electromagnetic and structural analysis engineering communities, no such paradigm exists for ultrasound researchers and engineers. This paper demonstrates a software package, Wave2000, which computes the full solution to the 2D viscoelastic wave equation. 2D objects are represented by graphical images and are comprised of a number of solids and/or liquids. Each material is specified in terms of its material density, the first and second Lame constants, and the first and second viscosities. The program computers the displacement vector was a function of Cartesian coordinates x and y and of time t, and the solution includes effects of diffraction, scattering, reflection, and attenuation of the propagating wave. Wave2000 implements a finite difference solution on a standard personal computer running Microsoft Windows 95 or NT. Sources and receivers may be located anywhere in or on the surface of the object. The source waveform can be practically any temporal function desired, including data collected from an actual transducer, and the receiver data can be sorted in a data file for subsequent processing. Several examples of the use of Wave2000 are given, including simulations of scattering from cracks and propagation through layers of materials and fluid-filled porous structures. Results demonstrate that computational methods can play an important can play an important role in NDT specifically and in ultrasonics in general.

A new dual-mode ultrasonic technique for assessing cortical bone

Osteoporotic fractures are a major public health problem; diagnosis is based on x-ray densitometry (DXA); however, DXA is not able to accurately predict who will and will not suffer a fracture. An alternative to DXA is ultrasound, which is viewed as having the potential to better characterize fracture risk. Our approach is based on “dual-mode“ ultrasound in which 2 distinct modes are used together to assess cortical bone. In particular, measurements are made at the mid-shaft tibia in both axial-transmission and pulse-echo modes. Axial transit time (τA) and pulse-echo transit time (τP/E) are obtained at the same tibial cortical site. These 2 transit times can be used in a classification scheme to identify individuals at greatest risk of fragility fracture. A pilot set of measurements on 5 individuals has been carried out to demonstrate the basic feasibility of the proposed technology. For the 5 subjects, each subject data point was found to be located in a distinct region (i.e., a hypothesized distinct bon...